Juan Estrada Fermilab

1
New preliminary measurement of the mass of the
top quark at DØ using Run I data

• Juan Estrada - Fermilab
• for the DØ Collaboration
• WC Seminar
• April 25, 2003

2
Overview

• The leptonjets decays of the top quark
• Introduction to the measurement of Mt
• Method used for this re-analysis
• Testing the analysis in simulated samples
• New preliminary Run I Mt measurement
• The mass of the W boson in the same sample
• Systematic uncertainties (JES)
• Conclusion

3
Lepton jets channel
30 of the total significantly less background
that the all jets channel.
Jet 3
Jet 4
Jet 2
Signature 1 charged lepton 4 jets Missing
energy
p
NOT detected
p
Jet 1
4
Leptonjets channel

• DØ Statistics Run I 125 pb-1
• Standard Selections
• Lepton Etgt20 GeV,?elt2,??lt1.7
• Jets ?4, ETgt15 GeV, ?lt2
• Missing ET gt 20 GeV
• ETW gt 60 GeV ?W lt2
• 91 events
• Ref. PRD 58 (1998), 052001
• After ?2(77 events) 29 signal 48 backg.
• (0.8 Wjets and 0.2 QCD)
• Specific cuts for this analysis
• 4 Jets only 71 events
• Background Prob. 22 events

5
Top Mass
For those of you who did not try to measure
Mt, this is how the mass distributions looks
like. It is a challenging problem and that is
why we have been applying sophisticated methods
making good use all the information that we have.
DØ , PRD 58 52001, (1998)
fitted mass
standard selection
6
Template method Previous DØ and CDF publications
Reducing the dimensionality of the problem A
multidimensional (xi) template is obtained for
each value of the input mass, and the data sample
is then compared with those MC templates to find
the most likely value for Mt
Template(xiMtB)
Template(xiMtA)

• Some limitations
• prescribed permutation is selected on basis of a
  kinematic fit.
• few variables, containing most of the
  information, are selected for the templates.
• single template fits the whole sample.

Sample probabilities
Data gt MtB
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DØ measurement using templatesPRD 58 52001,
(1998)
2D templates (NN, fitted mass)
Discriminator
MC studies give 8 GeV resolution
mfit (GeV)
Fit to data sample
Discriminator
100 200 mfit (GeV)
mfit (GeV)
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Measurement of Mt, two alternatives
Maximize
Simple case with several types of events, each
type follows a Gaussian distribution with width
sk and mean M0.
using templates
But, if possible, it will be better to calculate
a probability for each individual event
event weight depends on mi
correct weighted average!!
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Measurement of Mt, two alternatives

• If you have to choose between templates and
  event probabilities, consider the following
  points
• The the greater the variation between the events
  the greater the difference in the two methods
• For templates you could actually introduce larger
  fluctuation if you add to your sample low quality
  events (large sk), this will never happen for the
  correctly weighted average.
• ..note that there is no reason why analysis of
  same sample with two different methods should
  give you the same result, because methods are not
  totally correlated.

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Measurement of Mt using event probability

• ok, the event probabilities are better.
• How do we calculate the events probabilities?
• (for templates, we just use MC simulation of the
  detector)
• The standard model predicts these probabilities
  (differential cross section) in terms of the
  parton level quantities (four-vectors of all
  partons involved), but we do not have access to
  parton level quantities for events in our data
  sample.
• We will use only LO calculations, and I will
  show how far we can get with that. I will also
  show some problems due to our LO approximation

11
Measurement of Mt using event probability(before
we get into de details)
The probability for each event being signal is
calculated as a function of the top mass. The
probability for each event being background is
also calculated. The results are combined in one
likelihood for the sample. (Similar to the
methods of Dalitz, Goldstein and Kondo, Mt
measurement in the dilepton channel by DØ - PRD
60 52001 (1999) and idea by Berends et al for
WW- production.)
P(mt)
background event
signal event
P
?
Mt
Mt
Mt
Mt
Mt
Mt
Mt
Mt
Mt
Psignal
Pbackground
Psignal
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Three differences between the two approaches
Template Method
This analysis

• All the events are presented to the same
  template. Average probability distribution.
• The template corresponds to a probability
  distribution for the entire sample, using
  selected variables calculated from MC
  simulations.
• The features of individual events are averaged
  over the variables not considered in the template.

• Each event has its own probability distribution.
• The probability depends on all measured
  quantities (except for unclustered energy).
• Each event contributes with its own specific
  features to the probability, which depends how
  well is measured.

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Calculation of signal probability

• If we could access all parton level quantities
  in the events ( the four momentum for all final
  and initial state particles), then we would
  simply evaluate the differential cross section as
  a function of the mass of the top quark for these
  partons. This way we would be using our best
  knowledge of the physics involved.

Since we do not have the parton level
information for data, we use the differential
cross section and integrate over everything we do
not know.
14
Transfer function W(x,y)
W(x,y) probability of measuring x when y was
produced (x jet variables, y parton variables)
where Ey energy of the
produced quarks Ex measured
and corrected jet energy pye
produced electron momenta pxe
measured electron momenta ?y j
?xj produced and measured jet angles
Energy of electrons is considered well measured,
an extra integral is done for events with muons.
Due to the excellent granularity of the D?
calorimeter, angles are also considered as well
measured. A sum of two Gaussians is used for the
jet transfer function (Wjet), parameters
extracted from MC simulation.
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Probability for tt events (d?)
2(in) 18(final) 20 degrees of freedom 3(e)
8(?1..?4) 3(PinPfinal)1(EinEfinal) 15
constraints 20 15 5 integrals Sum over 24
combinations of jets, all values of the neutrino
momentum are considered. Because it is L.O., we
use only 4-jet events. ?1 momentum
of one of the jets m1,m2 top mass in the
event M1,M2 W mass in the event f(q1),f(q2)
parton distribution functions (CTEQ4) for qq
incident chann. q1,q2 initial parton
momenta ?6 six particle phase
space W(x,y) probability of measuring x when
y was produced in the collision We choose these
variables of integration because M2 is almost
negligible, except near the four peaks of the
Breit-Wigners within M2.
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Transfer function Wjet(x,y)
Models the smearing in jet energies from effects
of radiation, hadronization, measurement
resolution and jet reconstruction algorithm
asymmetries
Correcting on average, and considering these
distributions to be single Gaussians, can
underestimate parton energies
Use 2 Gaussians, one to account for the peak and
the other to fit the asymmetric tails (light
quarks and b quarks have separate parameters).
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Transfer function in ttbar
Top Mass
Histogram HERWIG events after full DØ
reconstruction, using the standard
criteria Solid Line Calculated by using the
transfer function on partons Dashed Same as
solid, but with a variant transfer function
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Transfer Function in Wjets
3 jets invariant mass
Invariant mass of three jets using W4-jets
events from VECBOS ISAJET (Smooth curve, same
as before). The shape is reproduced. any bias
introduced by non perfect agreement is calibrated
using MC simulations.
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Acceptance Corrections
Likelihood
Detector Acceptance
Measured probability
Detector acceptance
Production probability
where
, Ngen(N) is number of generated(observed) events
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Signal and Background

• The background probability is defined only in
  terms of the main backgound (Wjets, 80) which
  proves to be also adequate for multijet
  background treatment in this analysis.
• The background probability for each event is
  calculated using VECBOS subroutines for Wjets.
• The values of c1 and c2 are optimized, and the
  likelihood is normalized automatically at each
  value of ?.

21
Background Probability
We extracted from VECBOS events simulator the
subroutines that calculate the matrix element for
W4 jets events. W. Giele helped showing us the
way to use these subroutines. For this
probability we use MC integration
We integrate until we ensure the convergence.
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Background Probability
We extracted from VECBOS events simulator the
subroutines that calculate the matrix element for
W4 jets events. W. Giele helped showing us the
way to use these subroutines. For this
probability we use MC integration
We integrate until we ensure the convergence.
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Testing this in Run I DØ using full MC
Examples of product likelihood functions. Each
example corresponds to one experiment with the
statistics that DØ collected during Run I. The
signal(HERWIG) and background (VECBOS) events
were run through the full DØ Run I simulation.
24
Blind Analysis
This analysis was defined by MC studies, without
looking at the data sample. One of the checks
indicated that there could be a shift introduced
by background contamination.
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Extra selection in Pbkg
Wjets
Pbkglt1E-11
ttbar_at_175GeV
In order to increase the purity of signal,
another selection is applied on Pbkg, with
efficiencies ?signal 0.70, ?Wjets 0.30,
?multijets 0.23
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Blind Analysis, purified sample
0.5 GeV shift
This analysis was defined by MC studies, without
looking at the data sample. One of the checks
indicated that there could be a shift introduced
by background contamination.
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Crosscheck of linearity of response
Test of linearity of response with MC samples
containing large numbers of events.
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Probabilities in Data
Background probability
Discriminator
Comparison of (16 signal 55 background) MC and
data sample before the background probability
selection.
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Top probability in the background region
-ln(Ptt) as a function of Mt for 10-9ltPbkg
lt10-8
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Top probability for signal region
-ln(Ptt) as a function of Mt for 10-12ltPbkg
lt10-11
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New Preliminary Result
Mt 180.1 ? 3.6 GeV ? SYST - preliminary This
new technique improves the statistical error on
Mt from 5.6 GeV PRD 58 52001, (1998) to 3.6
GeV. This is equivalent to a factor of 2.4 in
the number of events. 22 events pass our cuts,
from fit (12 s 10 b) (0.5 GeV shift has been
applied, from MC studies)
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MC studies with 12s10b
The MC simulations show that the results obtained
are consistent with expectations.
33
Varying the background probability selection
The result is very stable with respect to the
selection on background probability.
34
Comparing results in data and MC
stat.err.
GeV
uncertainty from JES
mass
data
expected
PRD 58 52001, (1998)
(new)
Number of top decays
PRD 58 52001, (1998) 71 events NN 24
8 LB 29 8
New 22 events nS 12 4 (measured
sample) corrections0.70(4 jets)x0.71 (Pb) NS
25 7 (in the 1998 sample)
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Compatibility between 1998 and 2003

• Assume there is no systematic difference between
  the two methods
• and that both methods give an unbiased
  measurement of Mt .
• 1998 (24 events) ?(173.3 5.6) GeV
  
• 2003 (12 ev. subsample) ?(180.1 3.6) GeV
• If the methods were the same and all the events
  had the same
• resolution s245.6 ? s127.9, the fluctuations
  is 24 events when you
• vary only 12 is s12/247.9/24.0 ? the difference
  is therefore 1.7 s
• 2. Both methods are not the
• same (see introduction), and
• all the events have their own
• width, no reason to expect the
• same result even with the same
• sample. Simple case, s12/245.0,
• ? the difference is 1.4 s

36
Check of Mw with DØ Run I Data
80.9 2.6 GeV
Can help reduce the uncertainty in the jet energy
scale (JES) seehttp//dpf2002.velopers.net/talks_
pdf/120talk.pdf (DPF2002 proceedings) 1.5 GeV
shift is applied and 20 increase in the error,
from MC studies. We associate this shift to
effects from our L.O. approximation.
37
Number of events for signal and backg(something
to consider in the future)
Because of radiation, 20 of the signal events
look more like background than signal. When only
events with good jet-parton matching are used,
this is resolved (better treatment of higher
order effects will help).
38
MW, MC studies
We see that the signal events that are
reconstructed as background are responsible for
the 1.5 GeV shift in MW. This will have to be
solved if we want high precision top physics (1
GeV). Higher order corrections will have to be
included.
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Jet Energy Scale (main systematic effect)

• We use a Monte Carlo simulation of the detector
  to build the transfer function (or the templates
  in our previous analysis).
• It is essential to check that the energy scale
  in the MC simulation is representative of that in
  the detector. This can be done for the
  electromagnetic showers using Z?ee- decays. It
  is not so easy to do for hadronic showers.
• Our ?jet sample gives 2.5 uncertainty in JES.
  In 1998 this translated to 4.0 GeV in Mt.

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Systematic Uncertainty JES(presented HCP2002)
Using a sample of ?jet PRD 58 52001, (1998) we
got a function that matches the JES in MC and
data with 2.50.5 GeV uncertainty per jet. For
the result presented in HCP2002 (analysis tools
session), we did the analysis of data with and
without this correction. This was a very
conservative approach, because we just wanted to
demonstrate the statistical power of the
analysis.
1 2 ?
Et? (GeV)
41
Systematic error due to JES
For the result presented here, we are using the
previous calibration and its uncertainty for each
jet (2.50.5 GeV). ?JES3.3 GeV
Consistent with MC expectations
42
Systematic uncertainty due to top-production model
u fraction of events in the experiment where all
the jets can be matched with partons from top
quark decays. Increasing the fraction u,
effectively turns on radiation and hadronization
effects. The systematic uncertainty is ?1.5
GeV (Each point corresponds to the maximum of a
likelihood for a large event sample).
Herwig MC with official DØ simulation
43
Total Uncertainty

• I. Determined from MC studies with large event
  samples

II. Determined from data
Total systematic 4.0
GeV Mt 180.1 5.4 GeV (preliminary)
44
New preliminary Result
The relative error in this result is 3, compare
to 2.9 from the previous CDF and DØ combined
average for all channels.
45
Conclusions

• Using LO approximation (and parameterized
  showering) we calculated the event probabilities,
  and measured
• Mt180.1 ? 3.6 (stat) ? 4.0 (syst) GeV
  preliminary
• Significant improvement to our previous
  analysis, is equivalent to 2.4 times more data
• Correct permutation is always considered (along
  with the other eleven)
• All features of individual events are included,
  thereby well measured events contribute more
  information than poorly measured events.
• To consider for the future
• The possibility of checking the value of the W
  mass in the hadronic branch on the same events
  provides a new handle on controlling the largest
  systematic error, namely, the jet energy scale.
• A very general method (application to W boson
  helicity, Higgs searches, . )